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junior college 2 | H2 Maths

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i thought this was a right tail test because of the phrase “test if the manufacturer’s claim is valid” so i based the alternative hypothesis on the manufacturer’s claim. however the answer says it’s left tail but i still do not get it. thanks in advance :)

(Reposted from https://www.statisticshowto.datasciencecentral.com/probability-and-statistics/hypothesis-testing/ )

A principal at a certain school claims that the students in his school are above average intelligence. A random sample of thirty students IQ scores have a mean score of 112. Is there sufficient evidence to support the principal’s claim? The mean population IQ is 100 with a standard deviation of 15.

Step 1: State the Null hypothesis. The accepted fact is that the population mean is 100, so: H0: μ = 100.

Step 2: State the Alternate Hypothesis. The claim is that the students have above average IQ scores, so: H1: μ > 100.

In this case, the population mean is given and is accepted as a fact. But this principal thinks his students are above average. Based on the sample of his students, we try to see if his students are really smarter than average or it's just due to chance.

So we test the odds that's it's by chance.

The alternative hypothesis is that the IQ is actually higher than 100.

But in the case of your question, the population mean is not actually known or given. The manufacturer just claims that the population mean weight is ≥ 502g.

Remember that the null hypothesis is always the accepted fact, and the alternative hypothesis is trying to show otherwise.

If one were to simply trust the manufacturer, that means he/she accepts this as a fact and that it's true.

So, the null hypothesis would be that of the manufacturer's claim is true and is accepted as a fact. But we think otherwise. So we try to test the odds that the sample's results are by chance.

So the alternative hypothesis would be that the mean weight < 502g and is really lower than claimed (the accepted fact).

So it's a left tailed test.

The claim isn't always the alternative hypothesis. You have to exercise discretion and be careful about such questions, which can be tricky.

The null hypothesis is equal to 502. Assuming manufacturer is correct.

The alternative is less than 502 since the mean is 499 which is less than 502. This statement assumes the alternative is correct.

Generally, null is 'population' claim while alternative is 'sample' claim. If you do not reject null hypothesis, then the manufacturer claim is valid.